Evaluation and optimal management of patients with known or suspected ischemic cardiomyopathy requires an assessment of the magnitude and extent of myocardial ischemia as well as the extent of myocardial infarction and scar. While PET myocardial perfusion imaging offers the most robust method to evaluate the presence and severity of ischemia, it is currently limited by the degradation due to both cardiac and respirator motion. On the other hand, cardiac MR (CMR) currently offers the most accurate method to detect the presence and assess the extent of myocardial scar. It can also identify clinically important late gadolinium enhancement patterns associated with various non-ischemic cardiomyopathies and provides an assessment of global and regional wall motion abnormalities. Furthermore, CMR can be used to estimate the transmural extent of a given infarct, which directly correlates with the likelihood of recovery post coronary revascularization, and thus accurately identifies viable myocardium. However, quantification of the severity of ischemia, particularly when concomitant scar is also present, is less established with CMR. In order to take advantage of the inherent strengths of each technique and resolve fundamental limitations of these modalities, we propose to use simultaneous PET-MR to provide a comprehensive assessment of viable myocardium as well as an assessment of residual ischemia in patients with non-transmural infarctions. We will develop a novel list-mode PET reconstruction framework that incorporates cardiac and respiratory motion measured by MR into PET emission system matrix as well as the time-dependent attenuation map and the position dependent point spread function.